# Sliding Hockey Puck

1. Sep 6, 2012

### kchurchi

1. The problem statement, all variables and given/known data
A hockey puck is sliding across a frozen pond with an initial speed of 7.5 m/s. It comes to rest after sliding a distance of 23.7 m. What is the coefficient of kinetic friction between the puck and the ice?

v0x = initial speed = 7.5 m/s
vfx = final speed = 0 m/s
Δx = x distance traveled = 23.7 m
fk,IP = force of kinetic friction from ice on puck
NIP = normal force from ice on puck
WEP = weight force from earth on puck
mP = mass of puck
g = acceleration due to gravity

2. Relevant equations
ƩFnet = m*a
ƩFx = -fk,IP = m*ax
ƩFy = NIP - WEP = m*ay → ay = 0 m/s^2 → NIP = mP*g

3. The attempt at a solution
I attempted this logic...

fk,IP = μk*NIP → (-m*ax)/(mP*g) = μk

But then I hit a wall when trying to find the x-acceleration. Help?

2. Sep 6, 2012

### voko

You need the equation of distance traveled under constant acceleration (deceleration in this case).

3. Sep 18, 2012

### kchurchi

I am not allowed to have the equations of constant acceleration to solve problems. I must derive all equations myself using calculus. How do I even know that the acceleration is constant?

4. Sep 18, 2012

### SHISHKABOB

there's only one force acting on the puck in the x-direction: the frictional force

and it depends on two constant values: the coefficient of friction and the normal force on the puck

therefore, the force is constant, therefore the acceleration is constant

set up the equation of motion

$\Sigma F = m\ddot{x} = F_{friction}$

and go from there

I'm assuming that since they want you to derive the equations yourself, that you know how to do a differential equation, right?